Problem: Baby Ehab was toying around with arrays. He has an array a of length n. He defines an array to be good if there's no way to partition it into 2 subsequences such that the sum of the elements in the first is equal to the sum of the elements in the second. Now he wants to remove the minimum number of elements in a so that it becomes a good array. Can you help him?

A sequence b is a subsequence of an array a if b can be obtained from a by deleting some (possibly zero or all) elements. A partitioning of an array is a way to divide it into 2 subsequences such that every element belongs to exactly one subsequence, so you must use all the elements, and you can't share any elements.

Input

The first line contains an integer n (2 ≤ n ≤ 100) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_{n} (1 ≤ a_i ≤ 2000) — the elements of the array a.

Output

The first line should contain the minimum number of elements you need to remove.

The second line should contain the indices of the elements you're removing, separated by spaces.

We can show that an answer always exists. If there are multiple solutions, you can print any.

Examples

Input


4
6 3 9 12


Output


1
2

Input


2
1 2


Output


0

Note

In the first example, you can partition the array into [6,9] and [3,12], so you must remove at least 1 element. Removing 3 is sufficient.

In the second example, the array is already good, so you don't need to remove any elements.

Solution (in JAVA):

Solution:

import java.util.*;
import java.io.*;
import java.math.BigInteger;
public class Main {
	//  Solution 
   public static void main(String args[])
	{int n=in.nextInt();
	int[] a=in.arr(n);
	boolean[] canReach=new boolean[2001*100];
	canReach[0]=true;
	for (int cost:a) {
		for (int to=canReach.length-cost-1; to>=0; to--) {
			if (!canReach[to]) continue;
			canReach[to+cost]=true;
		}
	}
	int sum=0;
	for (int i:a) sum+=i;
	if (!canReach[sum/2] || sum%2!=0) {
		System.out.println(0);
		return;
	}
	int trailingZeros=31;
	for (int i:a) trailingZeros=Math.min(trailingZeros, Integer.numberOfTrailingZeros(i));
	int ans=-2;
	for (int i=0; i<n; i++) {
		if (a[i]%(1<<trailingZeros+1)!=0) ans=i;
	}
	System.out.println(1+"\n"+(ans+1));
}

static void sort(int[] a) {
	ArrayList<Integer> l=new ArrayList<>();
	for (int i:a) l.add(i);
	Collections.sort(l);
	for (int i=0; i<a.length; i++) a[i]=l.get(i);
}
   static boolean is_prime(int n) {
	   
	   if(n%2==0)
		   return false;
	   for (int i = 3; i * i<= n; i+=2) {
		if(n%i==0)
			return false;
	}
	   
	   return true;
   }
    static long mod=1000000007L;
    static long gcd(long a,long b) {
    	if(a==0)
    		return b;
    	return gcd(b%a,a);
    }
    static long dp[][][];
   
    static Reader in=new Reader();
    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
    static class Reader 
    { 
        private InputStream mIs;private byte[] buf = new byte[1024];private int curChar,numChars;public Reader() { this(System.in); }public Reader(InputStream is) { mIs = is;} 
        public int read() {if (numChars == -1) throw new InputMismatchException();if (curChar >= numChars) {curChar = 0;try { numChars = mIs.read(buf);} catch (IOException e) { throw new InputMismatchException();}if (numChars <= 0) return -1; }return buf[curChar++];} 
        public String nextLine(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isEndOfLine(c));return res.toString() ;} 
        public String s(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isSpaceChar(c));return res.toString();} 
        public long l(){int c = read();while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }long res = 0; do{ if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read();}while(!isSpaceChar(c));return res * sgn;} 
        public int nextInt(){int c = read() ;while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }int res = 0;do{if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read() ;}while(!isSpaceChar(c));return res * sgn;} 
        public double d() throws IOException {return Double.parseDouble(s()) ;}
        public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; } 
        public boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; } 
        public int[] arr(int n){int[] ret = new int[n];for (int i = 0; i < n; i++) {ret[i] = nextInt();}return ret;}
    }
}
class node implements Comparable<node> {
int val,pos;
node(int val,int pos){
	this.pos=pos;this.val=val;
}
@Override
public int compareTo(node o) {
	
	return val-o.val;
}
 
 
}
class xtree{
	public xtree(int n,int a[]) {
		this.a=a;
		seg=new int[n*4];
		//lazy=new int[n*4];
		build(1,0,n-1);
	}
	int seg[], a[],lazy[];
	    void check(int p,int s,int e) {
	        if(lazy[p]!=0) {
	            seg[p] += lazy[p];
	            if(s!=e) {
	                lazy[2*p] += lazy[p];
	                lazy[2*p+1] += lazy[p];
	            }
	            lazy[p] = 0;
	        }
	    }
	    
	     void build(int p,int s,int e) {
	        //check(p,s,e);
	        
	        if(s==e) {
	            seg[p] = a[s];
	            return;
	        }
	        
	        build(2*p,s,(s+e)/2);
	        build(2*p+1,(s+e)/2+1,e);
	        
	        seg[p] = seg[2*p]+ seg[2*p+1];
	    }
	    
	   void update(int p,int s,int e,int i,int v) {
	       // check(p,s,e);
	        
	        if(s==e) {
	            seg[p] = v;
	            return;
	        }
	        
	        if(i<=(s+e)/2) update(2*p,s,(s+e)/2,i,v);
	        else update(2*p+1,(s+e)/2+1,e,i,v);
	        
	        seg[p] = seg[2*p]+seg[2*p+1];
	    }
	    
	     void update(int p,int s,int e,int a,int b,int v) {
	        //check(p,s,e);
	        
	        if(s>=a && e<=b) {
	            seg[p] += v;
	            
	            if(s!=e) {
	                lazy[2*p] += v;
	                lazy[2*p+1] += v;
	            }
	            
	            return;
	        }
	        
	        if(s>b || e<a)
	            return;
	        
	        update(2*p,s,(s+e)/2,a,b,v);
	        update(2*p+1,(s+e)/2+1,e,a,b,v);
	        
	        seg[p] = seg[2*p]+seg[2*p+1];
	    }
    
 
    
    int get(int p,int s,int e,int a,int b) {
        if(s>=a && e<=b)
            return seg[p];
        
        if(s>b || e<a)
            return 0; 
        
        return get(2*p,s,(s+e)/2,a,b)+ get(2*p+1,(s+e)/2+1,e,a,b);
    }
}
 
class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
}
 
class Sorting{
 
 public static long[] bucketSort(long[] array, int bucketCount) {
 
 if (bucketCount <= 0) throw new IllegalArgumentException("Invalid bucket count");
 
 if (array.length <= 1) return array; //trivially sorted
 
 
 
 long high = array[0];
 
 long low = array[0];
 
 for (int i = 1; i < array.length; i++) { //find the range of input elements
 
 if (array[i] > high) high = array[i];
 
 if (array[i] < low) low = array[i];
 
 }
 
 double interval = ((double)(high - low + 1))/bucketCount; //range of one bucket
 
 
 ArrayList<Long> buckets[] = new ArrayList[bucketCount];
 
 for (int i = 0; i < bucketCount; i++) { //initialize buckets
 
 buckets[i] = new ArrayList();
 
 }
 
 
 
 for (int i = 0; i < array.length; i++) { //partition the input array
 
 buckets[(int)((array[i] - low)/interval)].add(array[i]);
 
 }
 
 
 int pointer = 0;
 
 for (int i = 0; i < buckets.length; i++) {
 
 Collections.sort(buckets[i]); //mergeSort
 
 for (int j = 0; j < buckets[i].size(); j++) { //merge the buckets
 
 array[pointer] = buckets[i].get(j);
 
 pointer++;
 
 }
 
}
 
return array;
 
}
}
 class LongestCommonSubsequence 
{ 
  
  /* Returns length of LCS for X[0..m-1], Y[0..n-1] */
	 int lcs( char[] X, char[] Y, int m, int n ,int K) 
	  { 
		 int L[][] = new int[m+1][n+1]; 
		 int ans[][]=new int[m+1][n+1];
		 int min[][] = new int[m+1][n+1]; 
		 for(int i=0;i<=n;i++) 
			 for(int j=0;j<=m;j++) 
				 min[j][i]='z'+1;
	    /* Following steps build L[m+1][n+1] in bottom up fashion. Note 
	         that L[i][j] contains length of LCS of X[0..i-1] and Y[0..j-1] */
	    for (int i=0; i<=m; i++) 
	    { 
	      for (int j=0; j<=n; j++)
	      { 
	        if (i == 0 || j == 0) 
	            L[i][j] = 0; 
	        else if (X[i-1] == Y[j-1]) { 
	            L[i][j] = L[i-1][j-1] + 1; 
	            ans[i][j]=ans[i-1][j-1]+X[i-1];
	         
	        }
	        else {
	            L[i][j] = max(L[i-1][j], L[i][j-1]); }
	      } 
	    } 
	  return L[m][n]; 
	  } 
	  
	  /* Utility function to get max of 2 integers */
	  int max(int a, int b) 
	  { 
	    return (a > b)? a : b; 
	  } 
 
     // Returns length of LCS for X[0..m-1], Y[0..n-1] 
     static String lcs(String X, String Y, int m, int n) 
     { 
         int[][] L = new int[m+1][n+1]; 
    
         // Following steps build L[m+1][n+1] in bottom up fashion. Note 
         // that L[i][j] contains length of LCS of X[0..i-1] and Y[0..j-1]  
         for (int i=0; i<=m; i++) 
         { 
             for (int j=0; j<=n; j++) 
             { 
                 if (i == 0 || j == 0) 
                     L[i][j] = 0; 
                 else if (X.charAt(i-1) == Y.charAt(j-1)) 
                     L[i][j] = L[i-1][j-1] + 1; 
                 else
                     L[i][j] = Math.max(L[i-1][j], L[i][j-1]); 
             } 
         } 
    
         // Following code is used to print LCS 
         int index = L[m][n]; 
         int temp = index; 
    
         // Create a character array to store the lcs string 
         char[] lcs = new char[index+1]; 
         lcs[index] = '\u0000'; // Set the terminating character 
    
         // Start from the right-most-bottom-most corner and 
         // one by one store characters in lcs[] 
         int i = m; 
         int j = n; 
         while (i > 0 && j > 0) 
         { 
             // If current character in X[] and Y are same, then 
             // current character is part of LCS 
             if (X.charAt(i-1) == Y.charAt(j-1)) 
             { 
                 // Put current character in result 
                 lcs[index-1] = X.charAt(i-1);  
                   
                 // reduce values of i, j and index 
                 i--;  
                 j--;  
                 index--;      
             } 
    
             // If not same, then find the larger of two and 
             // go in the direction of larger value 
             else if (L[i-1][j] > L[i][j-1]) 
                 i--; 
             else
                 j--; 
         } 
    
         // Print the lcs 
         StringBuilder Sd=new StringBuilder();
         for(int k=0;k<=temp;k++) 
             Sd.append(lcs[k]); 
      return Sd.toString();   
     }
 }